class: center, middle, inverse, title-slide .title[ # What are the effects of indirect facilitation on the dynamic of a dryland ecosystem? ] .subtitle[ ## Research associate application ] .author[ ### <strong>Alain Danet</strong>, Florian D. Schneider, Fabien Anthelme, Sonia Kéfi ] .author[ ### Illinois State University ] .author[ ### <a href="https://alaindanet.github.io">https://alaindanet.github.io</a> ] .date[ ### Slides created via the R package <a href="https://github.com/yihui/xaringan">xaringan</a> ] --- <div style = "position:fixed; visibility: hidden"> `$$\require{color}\definecolor{red}{rgb}{1, 0, 0}$$` `$$\require{color}\definecolor{green}{rgb}{0, 1, 0}$$` `$$\require{color}\definecolor{blue}{rgb}{0, 0, 1}$$` </div> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ TeX: { Macros: { red: ["{\\color{red}{#1}}", 1], green: ["{\\color{green}{#1}}", 1], blue: ["{\\color{blue}{#1}}", 1] }, loader: {load: ['[tex]/color']}, tex: {packages: {'[+]': ['color']}} } }); </script> <style> .red {color: #FF0000;} .green {color: #00FF00;} .blue {color: #0000FF;} </style> # Dryland ecosystems 41% of Earth land surface, 2bn of people <img src="data:image/png;base64,#fig_ymca/dryland_map.jpg" width="70%" style="display: block; margin: auto;" /> .footnote[[UNEP-WCMC](https://www.fao.org/dryland-assessment/en/), [IPCC report](https://www.ipcc.ch/srccl/chapter/chapter-3/)] <!--- knit those table chunk statements --> --- # Catastrophic shifts <img src="data:image/png;base64,#fig_ymca/catastrophic_shift1.png" width="70%" style="display: block; margin: auto;" /> .footnote[[Kéfi, et al. (2007)](http://www.sciencedirect.com/science/article/pii/S0040580906001250); [Scheffer, et al. (2001)](https://doi.org/10.1038/35098000); [Rietkerk, et al. (2004)](http://www.sciencemag.org/content/305/5692/1926)] --- # Catastrophic shifts <img src="data:image/png;base64,#fig_ymca/catastrophic_shift2.png" width="70%" style="display: block; margin: auto;" /> .footnote[[Kéfi, et al. (2007)](http://www.sciencedirect.com/science/article/pii/S0040580906001250); [Scheffer, et al. (2001)](https://doi.org/10.1038/35098000); [Rietkerk, et al. (2004)](http://www.sciencemag.org/content/305/5692/1926)] --- # Catastrophic shifts <img src="data:image/png;base64,#fig_ymca/catastrophic_shift3.png" width="70%" style="display: block; margin: auto;" /> .footnote[[Kéfi, et al. (2007)](http://www.sciencedirect.com/science/article/pii/S0040580906001250); [Scheffer, et al. (2001)](https://doi.org/10.1038/35098000); [Rietkerk, et al. (2004)](http://www.sciencemag.org/content/305/5692/1926)] --- # Catastrophic shifts <img src="data:image/png;base64,#fig_ymca/catastrophic_shift4.png" width="70%" style="display: block; margin: auto;" /> .footnote[[Kéfi, et al. (2007)](http://www.sciencedirect.com/science/article/pii/S0040580906001250); [Scheffer, et al. (2001)](https://doi.org/10.1038/35098000); [Rietkerk, et al. (2004)](http://www.sciencemag.org/content/305/5692/1926)] --- # Direct facilitation .footnote[[Callaway (2007b)](#bib-callaway_positive_2007); [Kéfi, et al. (2007)](http://www.sciencedirect.com/science/article/pii/S0040580906001250)] .pull-left[ <img src="data:image/png;base64,#fig_ymca/goodpatch-badpatch.jpg" width="70%" style="display: block; margin: auto;" /> ## Improving local conditions - Increasing resources - Limiting erosion - Limiting evapotranspiration ] .pull-right[ ## Positive feedback loop <div id="htmlwidget-d32c6820a5f9f6feeb3a" style="width:70%;height:302.4px;" class="grViz html-widget"></div> <script type="application/json" data-for="htmlwidget-d32c6820a5f9f6feeb3a">{"x":{"diagram":"\ndigraph boxes_and_circles {\n\n # a \"graph\" statement\n graph [overlap = true, fontsize = 18, fontname = FiraSans]\n\n node [shape = circle, fixedsize = true, width = 0.9]\n Vegetation;Water\n\n edge [penwidth=2, headport=\"nw\", tailport=\"sw\", label=\"+\"]\n Vegetation -> Water\n edge [penwidth=2, headport=\"se\", tailport=\"ne\", label=\"+\"]\n Water -> Vegetation\n}\n","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script> ] --- class: center # Overgrazing <img src="data:image/png;base64,#fig_ymca/brittannica.com.jpg" width="50%" style="display: block; margin: auto;" /> .footnote[[IPCC](https://www.ipcc.ch/srccl/chapter/chapter-3/), [brittannica.com](http://media-3.web.britannica.com/eb-media/55/20155-004-C8550C5E.jpg)] ??? Bisigato and Laphitz (2009) identified overgrazing as a cause of desertification in the Patagonian Monte region of Argentina Recent human-induced turning points in ecosystem functioning were uncovered around Volgograd (Russia) and around Lake Balkhash (Kazakhstan), attributed to recultivation, increased salinisation, and increased grazing. Successful grass establishment has been impeded by overgrazing and nutrient depletion leading to the encroachment of shrubs into the northern Chihuahuan Desert (USA) since the mid-19th century (Kidron and Gutschick 2017 ). --- # Indirect facilitation .footnote[Credit photo Fabien Anthelme, [Callaway (2007b)](#bib-callaway_positive_2007)] .pull-left[ <img src="data:image/png;base64,#fig_ymca/indirect_facilitation4.png" width="70%" style="display: block; margin: auto;" /> ] -- .pull-right[ <img src="data:image/png;base64,#fig_ymca/quercus_buxus.png" width="70%" style="display: block; margin: auto;" /> ] --- class: middle # Research question .footnote[[Verwijmeren, et al. (2013)](http://doi.wiley.com/10.1111/j.1600-0706.2012.00111.x)] ## Two different stress and two types of facilitation **What is the effect of indirect facilitation through grazing on the dynamic of a dryland ecosystem?** -- Coexistence, Stability, Cooccurrence --- class: center # Cellular automata .footnote[[Kéfi, et al. (2007)](http://www.sciencedirect.com/science/article/pii/S0040580906001250)] .pull-left[ <img src="data:image/png;base64,#fig_ymca/cyprus.jpg" width="70%" style="display: block; margin: auto;" /> ] .pull-right[ <img src="data:image/png;base64,#fig_ymca/random_landscape-eps-converted-to.png" width="70%" style="display: block; margin: auto;" /> ] --- background-image: url("data:image/png;base64,#fig_ymca/stand_alone.png") background-position: center background-size: contain # Cells --- # Transition equations - Mortality: $$ `\begin{aligned} w_{n,o} =& m \\ w_{p,o} =& m \end{aligned}` $$ -- - Degradation: $$ `\begin{aligned} w_{o,-} =& d \end{aligned}` $$ -- - Regeneration: $$ `\begin{aligned} w_{-,o} =& r + f q_{+|-} \end{aligned}` $$ -- `\(q_{i|j}\)`: proportion of i cells around j cells (local neighborhood) <!--- knit those table chunk statements --> --- # Colonization equations - Nurse colonization: `$$\begin{aligned}w_{o,n}=& (\red{\delta\rho_{n}} + (1-\delta)q_{n|o}) (b - c\rho_+ - \gamma)\end{aligned}$$` - Protegee colonization: `$$\begin{aligned}w_{o,p}=& (\red{\delta\rho_{p}} + (1-\delta)q_{p|o}) (b - c\rho_+ - g(1 - p))\end{aligned}$$` Mecanism: .red[Global dispersal] --- # Colonization equations - Nurse colonization: `$$\begin{aligned}w_{o,n}=& (\delta\rho_{n} + \red{(1-\delta)q_{n|o}}) (b - c\rho_+ - \gamma)\end{aligned}$$` - Protegee colonization: `$$\begin{aligned}w_{o,p}=& (\delta\rho_{p} + \red{(1-\delta)q_{p|o}}) (b - c\rho_+ - g(1 - p))\end{aligned}$$` Mecanism: .red[Local dispersal] --- # Colonization equations - Nurse colonization: `$$\begin{aligned}w_{o,n}=& (\delta\rho_{n} + (1-\delta)q_{n|o}) (\red{b} - c\rho_+ - \gamma)\end{aligned}$$` - Protegee colonization: `$$\begin{aligned}w_{o,p}=& (\delta\rho_{p} + (1-\delta)q_{p|o}) (\red{b} - c\rho_+ - g(1 - p))\end{aligned}$$` Mecanism: .red[Maximum survival and germination] --- # Colonization equations - Nurse colonization: `$$\begin{aligned}w_{o,n}=& (\delta\rho_{n} + (1-\delta)q_{n|o}) (b - \red{c\rho_+} - \gamma)\end{aligned}$$` - Protegee colonization: `$$\begin{aligned}w_{o,p}=& (\delta\rho_{p} + (1-\delta)q_{p|o}) (b - \red{c\rho_+} - g(1 - p))\end{aligned}$$` Mecanism: .red[Global competition for resources] --- # Colonization equations - Nurse colonization: `$$\begin{aligned}w_{o,n}=& (\delta\rho_{n} + (1-\delta)q_{n|o}) (b - c\rho_+ - \red{\gamma})\end{aligned}$$` - Protegee colonization: `$$\begin{aligned}w_{o,p}=& (\delta\rho_{p} + (1-\delta)q_{p|o}) (b - c\rho_+ - g(1 - p))\end{aligned}$$` Mecanism: .red[Cost of defense against grazing] --- # Colonization equations - Nurse colonization: `$$\begin{aligned}w_{o,n}=& (\delta\rho_{n} + (1-\delta)q_{n|o}) (b - c\rho_+ - \gamma)\end{aligned}$$` - Protegee colonization: `$$\begin{aligned}w_{o,p}=& (\delta\rho_{p} + (1-\delta)q_{p|o}) (b - c\rho_+ - \red{g(1 - p)})\end{aligned}$$` Mecanism: .red[Grazing and indirect facilitation] <!--- knit those table chunk statements --> --- class: center # Pair approximation <img src="data:image/png;base64,#fig_ymca/pair-approx2.png" width="70%" style="display: block; margin: auto;" /> --- class: center middle # Question How does indirect facilitation affect coexistence between two species in competition? --- # Coexistence Indirect facilitation allows coexistence between two species in competition <img src="data:image/png;base64,#fig_ymca/danet2020fig2.png" width="60%" style="display: block; margin: auto;" /> --- # Interpretation .footnote[[Holt, et al. (2017)](https://doi.org/10.1146/annurev-ecolsys-110316-022628)] .pull-left[ ## Classic apparent competition Herbivore maintains coexistence <img src="data:image/png;base64,#fig_ymca/plant_plant_herbivore.png" width="70%" style="display: block; margin: auto;" /> ] .pull-right[ ## Indirect facilitation Nurse maintains coexistence <img src="data:image/png;base64,#fig_ymca/nurse_protegee_herbivore.png" width="70%" style="display: block; margin: auto;" /> ] --- class: center middle # Question How does indirect facilitation affect stability along the aridity gradient? --- class: center # Stability .pull-left[ ## Without indirect facilitation <img src="data:image/png;base64,#fig_ymca/protegee_only_bifurc_g=0.25.png" width="100%" style="display: block; margin: auto;" /> ] -- .pull-right[ ## With indirect facilitation <img src="data:image/png;base64,#fig_ymca/bifurc_g=0.25_u=5.png" width="100%" style="display: block; margin: auto;" /> ] --- class: center middle # Question How does indirect facilitation affect cooccurrence between the nurse and the protegee? --- class: center middle # Cooccurrence We found that indirect facilitation does not affect the cooccurrence between the nurse and the protegee --- class: center # Take home message ## Indirect facilitation ... allows coexistence between two species in competition modifies the transition of the protegee along the aridity gradient does not necessarily affect species cooccurrence .footnote[[Danet, et al. (2020)](https://doi.org/10.1007/s12080-020-00489-0)] --- background-image: url("data:image/png;base64,#fig_ymca/merci.png") background-position: center background-size: contain # Thanks --- # Appendices --- # Cooccurrence .pull-left[ ## Clustering nurse protegee <img src="data:image/png;base64,#fig_ymca/clustering_u0_u10.png" width="90%" style="display: block; margin: auto;" /> ] -- .pull-right[ ## Nb of protegee | nurse <img src="data:image/png;base64,#fig_ymca/protegee_number_u0_u10.png" width="100%" style="display: block; margin: auto;" /> ]